In nuclear magnetic resonance (NMR), J-coupling is a measure of the effect the spin-state of one nucleus has on the chemical shift of another. Remember that in NMR, you're observing the absorbance of energy coupled to a change in alignment of the nuclear spin from parallel to antiparallel to the external magnetic field. J-coupling occurs when the amount of energy required to induce this spin-flip changes with the spin orientation of another nucleus. The coupling is measured and expressed (in Hertz) as the difference between the observed chemical shifts of the first nucleus when the second nucleus is in both of its possible spin states, and does not change with a change in the strength of the external magnetic field. (For the purposes of this discusion we will conveniently ignore the possibility that one or both of the nuclei have a spin larger than 1/2 as that is A) too complicated and B) not currently an issue in most comtemporary biomedical NMR.)

J-coupling is a direct measure of the orbital overlap between the two nuclei (see Molecular Orbital Theory.) As such it reflects only through-bond interactions (as opposed to the through-space interactions observed in the nuclear overhauser effect and dipolar coupling.) The magnitude of the the observed J-coupling depends on the identity of the nucleus the nucleus you're observing is coupled to (i.e. the second nucleus in the above explanation, but not the first.) as well as the nature of the covalent bond or bonds connecting the two.

Orbital overlap is also strongly dependent on symmetry. This means that the magnitude of the coupling observed between nuclei that are more than one bond apart is dependent on the angles between the bonds. The effect these torsion angles has on the observed J-coupling can be predicted with reasonable accuracy by a series of equations called the Karplus Equations. J-coupling is commonly used to help determine the 3-dimensional structures of relatively complicated molecules such as folded proteins, DNA and RNA with the help of these equations. One just measures the J-coupling between two nuclei a known number of bonds apart, and the Karplus Equations can tell you the possible angles those intervening bonds can take, thus greatly reducing the degeneracy (i.e. the number of possible structures) left over after the NOE mapping process.

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